{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:58Z","timestamp":1753893838720,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>For a permutation $\\pi=\\pi_1\\pi_2\\cdots\\pi_n\\in S_n$ and a positive integer $i\\leq n$, we can view $\\pi_1\\pi_2\\cdots\\pi_i$ as an element of $S_i$ by order-preserving relabeling. The $j$-set of $\\pi$ is the set of $i$'s such that $\\pi_1\\pi_2\\cdots\\pi_i$ is an involution in $S_i$. We prove a characterization theorem for $j$-sets, give a generating function for the number of different $j$-sets of permutations in $S_n$. We also compute the numbers of permutations in $S_n$ with a given $j$-set and prove some properties of them.<\/jats:p>","DOI":"10.37236\/921","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T23:54:12Z","timestamp":1578700452000},"source":"Crossref","is-referenced-by-count":1,"title":["The Initial Involution Patterns of Permutations"],"prefix":"10.37236","volume":"14","author":[{"given":"Dongsu","family":"Kim","sequence":"first","affiliation":[]},{"given":"Jang Soo","family":"Kim","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2007,1,3]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v14i1r2\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v14i1r2\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:05:30Z","timestamp":1579302330000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v14i1r2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,1,3]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2007,1,3]]}},"URL":"https:\/\/doi.org\/10.37236\/921","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2007,1,3]]},"article-number":"R2"}}